The cosmological constant (CC) problem [1]} (see, e.g., [2]}, [3]}, [4]}, [5]} for reviewsThe inspiring review [5]} is largely based on the previous works by the author and his collaborators (see, e.g., [7]}, [8]}, [9]}) that were further developed in [10]}, [11]}, [12]}. One of the main themes of these works is the so-called running vacuum. These works are further commented on in the conclusion and [13]}.) arises from the loop effects of Standard Model (SM) particles, such as the Higgs particle. Since the electroweak scale is much higher than, say, the temperature of the cosmic microwave background (CMB), it has been a standard practice to apply the zero-temperature setup to formulate and tackle the problem. However, since the CC, as vacuum energy, is an infrared effect (in the sense explained below) and thus governed by the low energy sector, the infrared structure of the theory must be important and its meticulous description is desirable.
The fact that the CC is a vacuum energy also implies that quantization and renormalization of gravity must be involved in its systematic treatment. In particular, the resolution of the problem would require renormalization of the vacuum energy. In this work we show that the finite temperature effects allow, when properly taken into account in the quantum gravitational setup, one to avoid the CC fine-tuning problem.
